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Homoclinic solutions for a difference equation with the mean curvature operator and periodic coefficients 具有平均曲率算子和周期系数的差分方程的同斜解
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-09-01 DOI: 10.1016/j.aml.2025.109737
Xiaoguang Li , Zhan Zhou
{"title":"Homoclinic solutions for a difference equation with the mean curvature operator and periodic coefficients","authors":"Xiaoguang Li ,&nbsp;Zhan Zhou","doi":"10.1016/j.aml.2025.109737","DOIUrl":"10.1016/j.aml.2025.109737","url":null,"abstract":"<div><div>We establish the existence of nontrivial homoclinic solutions for a class of difference equation with the mean curvature operator and periodic potentials via variational methods. Specifically, a novel approach inspired by the <em>vanishing</em> in the <em>concentration–compactness principle</em> is employed to prove the boundedness of Cerami sequences. Finally, we investigate the strict monotonicity and sign-definiteness of the obtained homoclinic solution, which have rarely been discussed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109737"},"PeriodicalIF":2.8,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Novel exponential-weighted integral inequality for exponential stability analysis of time-varying delay systems 时变时滞系统指数稳定性分析的指数加权积分不等式
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-09-01 DOI: 10.1016/j.aml.2025.109730
Nuo Cheng , Wei Wang , Hong-Bing Zeng , Xinge Liu , Xian-Ming Zhang
{"title":"Novel exponential-weighted integral inequality for exponential stability analysis of time-varying delay systems","authors":"Nuo Cheng ,&nbsp;Wei Wang ,&nbsp;Hong-Bing Zeng ,&nbsp;Xinge Liu ,&nbsp;Xian-Ming Zhang","doi":"10.1016/j.aml.2025.109730","DOIUrl":"10.1016/j.aml.2025.109730","url":null,"abstract":"<div><div>This paper investigates the exponential stability of systems with time-varying delays. A novel exponential-weighted integral inequality is developed from the extension of the second-order Bessel–Legendre inequality by introducing suitable coefficients into orthogonal polynomials, which leverages the monotonic property of certain integral ratios derived from orthogonal polynomials. This inequality enables the direct estimation of exponential-weighted integrals with varying limits, without requiring the additional conservative bounding commonly used in existing literature. Utilizing the proposed inequality, two exponential stability criteria are derived, corresponding to two different cases of time-varying delays. Simulations based on two well-studied examples demonstrate the effectiveness of the proposed approach.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109730"},"PeriodicalIF":2.8,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global boundedness in a three-species system with indirect prey-taxis 具有间接掠食性的三物种系统的全局有界性
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-08-31 DOI: 10.1016/j.aml.2025.109738
Qigang Deng, Ali Rehman, Ranchao Wu
{"title":"Global boundedness in a three-species system with indirect prey-taxis","authors":"Qigang Deng,&nbsp;Ali Rehman,&nbsp;Ranchao Wu","doi":"10.1016/j.aml.2025.109738","DOIUrl":"10.1016/j.aml.2025.109738","url":null,"abstract":"<div><div>It is showed that a fully parabolic three-species predator–prey model with indirect prey-taxis in a bounded domain has a globally bounded classical solution, which means the solution will not blow up. The results extend the previous ones in Zheng and Wan (2025). In the high-dimensional setting, conditions on parameters are further relaxed.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109738"},"PeriodicalIF":2.8,"publicationDate":"2025-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Oscillation theorems for linear Hamiltonian systems with nonlinear dependence on the spectral parameter and separated boundary conditions 具有谱参数和分离边界条件非线性依赖的线性哈密顿系统的振动定理
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-08-30 DOI: 10.1016/j.aml.2025.109740
Julia Elyseeva, Natalia Rogozina
{"title":"Oscillation theorems for linear Hamiltonian systems with nonlinear dependence on the spectral parameter and separated boundary conditions","authors":"Julia Elyseeva,&nbsp;Natalia Rogozina","doi":"10.1016/j.aml.2025.109740","DOIUrl":"10.1016/j.aml.2025.109740","url":null,"abstract":"<div><div>In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with separated boundary conditions. In our consideration we do not impose any controllability and strict normality assumptions and omit the Legendre condition for the Hamiltonian. The main results generalize our previous investigations for the Hamiltonian spectral problems with Dirichlet boundary conditions. We prove the local and global oscillation theorems relating the number of left finite eigenvalues of the problem in the given interval with the values of the oscillation numbers at the end points of this interval.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109740"},"PeriodicalIF":2.8,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the mathematical structure and solvability of certain Hilbert space optimization problems in data-driven elasticity 数据驱动弹性中某些Hilbert空间优化问题的数学结构和可解性
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-08-29 DOI: 10.1016/j.aml.2025.109739
Cristian G. Gebhardt , Marc C. Steinbach
{"title":"On the mathematical structure and solvability of certain Hilbert space optimization problems in data-driven elasticity","authors":"Cristian G. Gebhardt ,&nbsp;Marc C. Steinbach","doi":"10.1016/j.aml.2025.109739","DOIUrl":"10.1016/j.aml.2025.109739","url":null,"abstract":"<div><div>In this theoretical study, we analyze the structure and solvability of data-driven elasticity problems in one spatial dimension. In contrast to Conti, Müller, Ortiz (2018, 2020), who develop an extensive, highly abstract theory for mixed Dirichlet–Neumann problems in arbitrary dimension, our setting provides a direct understanding of the problem structure and of the key issue of existence of minimizers in Hilbert space on a basic technical level. For Dirichlet problems with low regularity, we derive a reduced problem defined on orthogonal subspaces, we give explicit representations of all relevant spaces and operators, and we exploit the orthogonal decomposition to prove solvability for several standard cases and under certain symmetries. For mixed Dirichlet–Neumann problems, we prove universal solvability. In addition, we address the issue of thermomechanical consistency.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109739"},"PeriodicalIF":2.8,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Space–time generalized finite difference scheme for three-dimensional unsteady nonlinear convection–diffusion–reaction equation 三维非定常非线性对流-扩散-反应方程的时空广义有限差分格式
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-08-29 DOI: 10.1016/j.aml.2025.109722
Fan Zhang, Po-Wei Li, Kexin Yi
{"title":"Space–time generalized finite difference scheme for three-dimensional unsteady nonlinear convection–diffusion–reaction equation","authors":"Fan Zhang,&nbsp;Po-Wei Li,&nbsp;Kexin Yi","doi":"10.1016/j.aml.2025.109722","DOIUrl":"10.1016/j.aml.2025.109722","url":null,"abstract":"<div><div>This paper develops a space–time generalized finite difference method (ST-GFDM), integrated with a time-marching framework and the Levenberg–Marquardt algorithm (LMA), to address three-dimensional unsteady nonlinear convection–diffusion–reaction equations. The ST-GFDM, as a meshless approach combined with a space–time formulation, approximates spatial and temporal derivatives by solving a local least-squares system derived from Taylor series expansion within the ST domain. Through this formulation, the governing PDEs are converted into a nonlinear algebraic system, efficiently resolved via a two-step LMA iteration. The time-marching mechanism incrementally propagates the ST computational domain forward along the temporal axis, which significantly reduces memory usage and enhances performance in long-duration simulations. The unified treatment of time and space discretization further improves numerical robustness, alleviating sensitivity to parameters that typically challenge conventional solvers in high-dimensional transient problems. Two benchmark tests are conducted to validate the effectiveness and applicability of the proposed meshless framework for solving 3D nonlinear convection–diffusion–reaction systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109722"},"PeriodicalIF":2.8,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A stochastic column-block gradient descent method for solving nonlinear systems of equations 求解非线性方程组的随机柱块梯度下降法
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-08-28 DOI: 10.1016/j.aml.2025.109735
Naiyu Jiang, Wendi Bao, Lili Xing, Weiguo Li
{"title":"A stochastic column-block gradient descent method for solving nonlinear systems of equations","authors":"Naiyu Jiang,&nbsp;Wendi Bao,&nbsp;Lili Xing,&nbsp;Weiguo Li","doi":"10.1016/j.aml.2025.109735","DOIUrl":"10.1016/j.aml.2025.109735","url":null,"abstract":"<div><div>In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We provide a thorough convergence analysis, and derive an upper bound for the convergence rate of the new method. Numerical experiments demonstrate that the proposed method outperforms the existing ones.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109735"},"PeriodicalIF":2.8,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constrained low-rank approximation of quaternion matrices and beyond 约束四元数矩阵的低秩逼近及以后
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-08-28 DOI: 10.1016/j.aml.2025.109724
Zhijie Wang , Liangtian He , Jifei Miao , Liang-Jian Deng , Jun Liu
{"title":"Constrained low-rank approximation of quaternion matrices and beyond","authors":"Zhijie Wang ,&nbsp;Liangtian He ,&nbsp;Jifei Miao ,&nbsp;Liang-Jian Deng ,&nbsp;Jun Liu","doi":"10.1016/j.aml.2025.109724","DOIUrl":"10.1016/j.aml.2025.109724","url":null,"abstract":"<div><div>Pure quaternion matrices have been widely used in color image processing. However, existing methods often overlook a fundamental fact: the pixels of an image in <span><math><mi>b</mi></math></span>-bit format can only take integer values from the set <span><math><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mo>…</mo><mo>,</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>b</mi></mrow></msup><mo>−</mo><mn>1</mn><mo>}</mo></mrow></math></span>. In this paper, we consider this important constraint and propose a constrained model that simultaneously incorporates the pure, integer and box constraints for low-rank quaternion matrix approximation. Our model can precisely obtain the optimal fixed-rank approximation while preserving these essential properties of quaternion matrices. Furthermore, we introduce a universal framework for constrained low-rank quaternion matrix completion tailored to color image inpainting, supported by rigorous theoretical convergence analysis. Experimental results demonstrate the superiority of our algorithms over state-of-the-art methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109724"},"PeriodicalIF":2.8,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A BEM framework for acoustic field analysis in ultra-thin coating/substrate structures 超薄涂层/衬底结构声场分析的边界元框架
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-08-28 DOI: 10.1016/j.aml.2025.109743
Haodong Ma , Qiang Wang , Wenzhen Qu
{"title":"A BEM framework for acoustic field analysis in ultra-thin coating/substrate structures","authors":"Haodong Ma ,&nbsp;Qiang Wang ,&nbsp;Wenzhen Qu","doi":"10.1016/j.aml.2025.109743","DOIUrl":"10.1016/j.aml.2025.109743","url":null,"abstract":"<div><div>This paper presents an advanced boundary element method (BEM) for high-precision analysis of two-dimensional acoustic fields in ultra-thin coating/substrate structures. The scaled coordinate transformation (SCT) method is first extended to acoustic analysis, enabling stable and efficient evaluation of domain integrals in ultra-thin coating systems without requiring domain discretization. The BEM is applied separately to the ultra-thin coating and substrate, generating boundary integral equations based on material-specific fundamental solutions, with continuity enforced through interface conditions. This BEM framework offers a potential alternative for modeling nanoscale acoustic fields, addressing the limitations in accuracy encountered by traditional numerical approaches. A comprehensive validation is performed by benchmarking against analytical solutions and results obtained by the COMSOL Multiphysics.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109743"},"PeriodicalIF":2.8,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Lagrange multiplier approach for general Hamiltonian PDEs 一般哈密顿偏微分方程的拉格朗日乘子方法
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2025-08-27 DOI: 10.1016/j.aml.2025.109734
Yonghui Bo , Yushun Wang
{"title":"The Lagrange multiplier approach for general Hamiltonian PDEs","authors":"Yonghui Bo ,&nbsp;Yushun Wang","doi":"10.1016/j.aml.2025.109734","DOIUrl":"10.1016/j.aml.2025.109734","url":null,"abstract":"<div><div>A novel linearly implicit energy-preserving scheme is proposed for general Hamiltonian PDEs by introducing the Lagrange multiplier approach. Unlike the previous scalar auxiliary variable (SAV) method, the new approach does not require the nonlinear part of the energy to be bounded from below, and conserves the original energy in both continuous and discrete cases. Moreover, the price we pay for these advantages is that a nonlinear algebraic equation has to be solved to determine the Lagrange multiplier. Combined with numerical experiments, where the computational cost of the Lagrange multiplier is generally not dominant, we show that the new scheme is computationally efficient as the SAV method, and that it accurately preserves the original energy.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"172 ","pages":"Article 109734"},"PeriodicalIF":2.8,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144918092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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